A sphere of diameter 7.0 cm and mass 266.5 g float in a bath of liquid. As the temperature is raised, the sphere begins to sink at a temperature of `35^0 C`. If the density of liquid is `1.527 g cm^(-3)` at `0^o C`, find the coefficient of cubical expansion of the liquid. Neglect the expansion of the sphere.

Explanation

The sphere will sink in the liqued at `35"^(@)C,` when its density becomes equal to the density of liquid at `30"^(@)C.` The density of sphere,
`P_(35)=(Mass)/(Volume)=(266.5)/((4)/(3)xx((22)/(7))xx((7)/(2))^(3))=1.483g//cm^(3)`
Now`" " P_(o)=P_(35)[1+gammaDeltaT]`
`1.527=1.483[1+gammaxx35]`
`1.029=1+gammaxx35`
`gamma=(1.209-1)/(35)=0.00083//"^(@)C`